Adaptive fuzzy output-feedback fault-tolerant tracking control of a class of uncertain nonlinear switched systems

ABSTRACT

This paper considers the output-feedback fault-tolerant tracking control problem for a class of uncertain nonlinear switched systems with nonlinear faults and strict-feedback form, where the faults which are nonaffine occur on the actuator. As a kind of specialised function approximating tool, fuzzy logic systems (FLSs), are employed to approximate the unknown smooth nonlinear functions. A switched fuzzy observer is designed to address the problem of unmeasurable states, filtered signals are used to address algebraic loop problem and the average dwell time (ADT) method is further utilised to prove the stability of the resulting closed-loop systems under a type of slowly switching signals. Based on the backstepping recursive design technique and Lyapunov function method, an adaptive fuzzy output-feedback control scheme is developed. The developed control method can ensure all the signals are semi-globally uniformly ultimately bounded (SGUUB) and the system output tracks the reference signal tightly even if unknown fault occurs. A simulation carried on an example demonstrates the validity of the obtained control scheme.     

非线性严格反馈系统自适应非反步输出反馈控制

针对传统反步控制器设计方法存在复杂度爆炸、参数收敛难、控制奇异、需全系统状态已知等问题,提出一种新的可保证参数收敛的未知系统动态辨识和非反步输出反馈自适应控制方法.首先,通过定义新的状态变量和系统等价变换,将严格反馈系统状态反馈控制转化为标准系统的输出反馈控制,进而设计包含高阶微分器的自适应单步控制器,避免反步递推设计的问题;然后,采用两个神经网络对系统集总未知动态进行估计,避免传统控制方法在未知控制增益在线估计过零引发的奇异问题;最后,构造一种新的自适应算法在线更新神经网络权值确保其收敛到真实值,进而实现对未知系统动态的精准辨识.基于Lyapunov定理的分析表明,跟踪误差和估计误差均可收敛到零点附近紧集.基于液压伺服系统模型的对比仿真验证了所提出方法的有效性和优越性.     

Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems

In this paper, the problem of decentralized adaptive output-feedback stabilization is investigated for large-scale stochastic nonlinear systems with three types of uncertainties, including parametric uncertainties, nonlinear uncertain interactions and stochastic inverse dynamics. Under the assumption that the inverse dynamics of the subsystems are stochastic input-to-state stable, an adaptive output-feedback controller is constructively designed by the backstepping method. It is shown that under some general conditions, the closed-loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability. In addition, the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin. The contributions of the work are characterized by the following novel features: (1) even for centralized single-input single-output systems, this paper presents a first result in stochastic, nonlinear, adaptive, output-feedback asymptotic stabilization; (2) the methodology previously developed for deterministic large-scale systems is generalized to stochastic ones. At the same time, novel small-gain conditions for small signals are identified in the setting of stochastic systems design; (3) both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states; (4) parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields, which may appear nonlinearly; (5) the concept of stochastic input-to-state stability and the method of changing supply functions are adapted, for the first time, to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control.     

Adaptive neural tracking control for a class of stochastic nonlinear systems

This paper investigates the problem of adaptive neural control design for a class of single‐input single‐output strict‐feedback stochastic nonlinear systems whose output is an known linear function. The radial basis function neural networks are used to approximate the nonlinearities, and adaptive backstepping technique is employed to construct controllers. It is shown that the proposed controller ensures that all signals of the closed‐loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of mean quartic value. The salient property of the proposed scheme is that only one adaptive parameter is needed to be tuned online. So, the computational burden is considerably alleviated. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

时变时滞随机非线性系统的自适应神经网络跟踪控制

针对一类具有时变时滞的不确定随机非线性严格反馈系统的自适应跟踪问题,利用Razumikhin引理和backstepping方法,提出一种新的自适应神经网络跟踪控制器.该控制器可保证闭环系统的所有误差变量皆四阶矩半全局一致最终有界,并且跟踪误差可以稳定在原点附近的邻域内.仿真例子表明所提出控制方案的有效性.     

Adaptive output-feedback control of nonlinear systems with unknown nonlinearities

In this paper, we consider global adaptive output-feedback control of nonlinear systems in output-feedback form, without a priori knowledge of system nonlinearities. Our proposed adaptive controller is a high-gain linear controller (since we have no knowledge on system nonlinearities), with the high-gain parameter tuned online via a switching logic. Global stability results of the closed-loop system have been proved.     

Adaptive tracking of stochastic nonlinear systems with Prandtl–Ishlinskii hysteresis

This paper deals with adaptive tracking problems for a class of stochastic nonlinear systems with unknown hysteresis nonlinearities. The system considered is in a strict‐feedback form driven by unknown Prandtl–Ishlinskii hysteresis and Wiener noises of unknown covariance. By employing backstepping design techniques and stochastic Lyapunov design method, parameter adaptive laws and control laws are obtained, which ensure that the tracking error can converge to a small residual set around the origin in the sense of mean quartic value. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive output feedback tracking control of stochastic nonlinear systems with dynamic uncertainties

In this paper, adaptive output feedback tracking control is developed for a class of stochastic nonlinear systems with dynamic uncertainties and unmeasured states. Neural networks are used to approximate the unknown nonlinear functions. K‐filters are designed to estimate the unmeasured states. An available dynamic signal is introduced to dominate the unmodeled dynamics. By combining dynamic surface control technique with backstepping, the condition in which the approximation error is assumed to be bounded is avoided. Using It ô formula and Chebyshev's inequality, it is shown that all signals in the closed‐loop system are bounded in probability, and the error signals are semi‐globally uniformly ultimately bounded in mean square or the sense of four‐moment. Simulation results are provided to illustrate the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust output-feedback control for stochastic nonlinear systems with modeling errors

In this paper,the stabilization problem of a stochastic nonlinear system with modeling errors is considered. An augmented observer is first presented to counteract the unmeasurable states as well as modeling errors.An adaptive output feedback controller is designed such that all signals in the closed-loop system are bounded in probability and the output is regulated to the origin almost surely.     

一类非线性时滞输出反馈系统的自适应控制

针对一类参数化非线性时滞输出反馈系统,提出了一种无记忆自适应跟踪控制器的设计方案.采用时滞滤波器估计系统状态,用Domination处理非线性时滞项,应用Backstepping技术设计控制器和参数自适应律.放宽了对时滞项的要求.通过构建一个Lyapunov＿Krasoviskii泛函,证明了闭环系统的稳定性,实现了对目标轨线的渐近跟踪,保证了所有信号一致有界.实例仿真说明了该方案的可行性.     

Adaptive output-feedback regulation for nonlinear delayed systems using neural network

A novel adaptive neural network （NN） output-feedback regulation algorithm for a class of nonlinear time-varying timedelay systems is proposed. Both the designed observer and controller are independent of time delay. Different from the existing results, where the upper bounding functions of time-delay terms are assumed to be known, we only use an NN to compensate for all unknown upper bounding functions without that assumption. The proposed design method is proved to be able to guarantee semi-global uniform ultimate boundedness of all the signals in the closed system, and the system output is proved to converge to a small neighborhood of the origin. The simulation results verify the effectiveness of the control scheme.     

Continuous output-feedback stabilization for a class of stochastic high-order nonlinear systems

This paper is concerned with the global stabilization via output-feedback for a class of high-order stochastic nonlinear systems with unmeasurable states dependent growth and uncertain control coefficients. Indeed, there have been abundant deterministic results which recently inspired the intense investigation for their stochastic analogous. However, because of the possibility of non-unique solutions to the systems, there lack basic concepts and theorems for the problem under investigation. First of all, two stochastic stability concepts are generalized to allow the stochastic systems with more than one solution, and a key theorem is given to provide the sufficient conditions for the stochastic stabilities in a weaker sense. Then, by introducing the suitable reduced order observer and appropriate control Lyapunov functions, and by using the method of adding a power integrator, a continuous (nonsmooth) output-feedback controller is successfully designed, which guarantees that the closed-loop system is globally asymptotically stable in probability.     

Minimal-order observer and output-feedback stabilization control design of stochastic nonlinear systems

1IntroductionTheproblemofestimatingtheparametersofmultiplesinusoidsinnoisehasre-ceivedconsiderableattentioninthepastthirtyyears,andalotofalgorithmshavebeenestablishedtosolvetheproblem.Amongallofthealgorithms,themaximumlikelihood(ML)estimatorisaprominentone[1],andseveralalgorithms,suchasANP[2]andIMP[3,4]arerelatedtoML.ThedrawbackoftheMLestimatorisitshighcomputationalcomplexity,sothealternatingprojection(AP)algorithm[5]wasdevelopedtomakeitsrealtimerealizationpossible.Butthefundamentaldefic…     

Global output-feedback stabilization for a class of stochastic non-minimum-phase nonlinear systems

In this paper, the problem of output-feedback stabilization is investigated for the first time for a class of stochastic nonlinear systems whose zero dynamics may be unstable. Under the assumption that the inverse dynamics of the system is stochastic input-to-state stabilizable, a stabilizing output-feedback controller is constructively designed by the integrator backstepping method together with a new reduced-order observer design and the technique of changing supply functions. It is shown that, under small-gain type conditions for small signals, the resulting closed-loop system is globally asymptotically stable in probability. The obtained results extend the existing methodology from deterministic systems to stochastic systems. An example is given to demonstrate the main features and effectiveness of the proposed output-feedback control scheme.     

非线性关联系统自适应神经网络输出反馈分散控制

针对一类带有完全未知关联项的非线性大系统,提出一种自适应神经网络输出反馈分散控制方法.采用神经网络逼近未知的关联项,因此对关联项常做的假设如匹配条件,被上界函数所界定等不再要求.在神经元输入中采用参考信号取代关联信号,从而成功地避免了对关联信号的微分.保证了闭环系统所有信号半全局一致最终有界,证明了跟踪误差收敛于一个包含原点的小残集.     

Global adaptive output-feedback tracking with prescribed performance for uncertain nonlinear systems

At present, one typical control strategy for guaranteeing transient and steady-state performance is funnel control and prescribed performance control. The strategy features completely discarding the system nonlinearities, even if they are completely known and available. Such an intrinsic feature requires the controller to produce a larger control effect to eliminate the negative impact caused by the high nonlinearities, leading to a conservative controller. In this paper, we fully take advantage...     

增长率为输出的未知多项式非线性系统的全局输出反馈跟踪

本文研究了一类增长线性地依赖于不可测状态非线性系统的输出反馈自适应实用跟踪问题.很不同的是,本文所研究系统的增长率是输出的未知多项式(系数未知、幂次已知),且关于被跟踪参考信号的假设相当弱(仅本身和其导数为已知的),为解决该问题,通过灵活采用通用控制和死区的思想和方法,引入了带有新型动态增益的观测器来重构不可测的系统状态,进而构造了自适应输出反馈跟踪控制器.可以证明,当控制器中的设计参数适当选取时,闭环系统所有状态有界,并且跟踪误差趋于事先给定的充分小的区域.数值仿真说明了所提方法的有效性.     

Adaptive neural tracking control for nonstrict-feedback stochastic nonlinear time-delay systems with full-state constraints

An adaptive neural tracking control is investigated for a class of nonstrict-feedback stochastic nonlinear time-delay systems with full-state constraints and saturation input. First, the continuous differentiable saturation model is employed to ensure the input constraint, and a barrier Lyapunov function is designed to achieve the full-state constraint. Second, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown time-delay terms, and neural networks are employed to approximate the unknown nonlinearities. Finally, based on Lyapunov stability theory, an adaptive controller is proposed to guarantee that all the signals in the closed-loop system are 4-Moment (or 2-Moment) semi-globally uniformly ultimately bounded and the tracking error converges to a small neighbourhood of the origin. Two examples are shown to further demonstrate the effectiveness of the proposed control scheme.     

Adaptive nonlinear output-feedback schemes with Marino-Tomeicontroller

Three new adaptive nonlinear output-feedback schemes are presented. The first scheme employs the tuning functions design. The other two employ a novel estimation-based design consisting of a strengthened controller-observer pair and observer-based and swapping-based identifiers. They remove restrictive growth and matching conditions present in the previous output-feedback nonlinear estimation-based designs and allow a systematic improvement of transient performance     

Adaptive event-triggered tracking control for a class of stochastic nonlinear systems with full-state constraints

This paper proposes an adaptive event trigger-based sample-and-hold tracking control scheme for a class of strict-feedback nonlinear stochastic systems with full-state constraints. By introducing a tan-type stochastic Barrier Lyapunov function (SBLF) combined with radial basis function neural networks (RBFNNs), which is used to approximate the nonlinear functions in backstepping procedures, an adaptive event-triggered controller is designed. It is shown with stochastic stability theory that all the states cannot violate their constraints, and Zeno behavior is excluded almost surely. Meanwhile, all the signals of the closed-loop systems are bounded almost surely and the tracking error converges to an arbitrary small compact set in the fourth-moment sense. A simulation example is given to show the effectiveness of the control scheme.